this should say
b + c = -b + 3c
add b to each side, subtract c
2b = 2c
Out of some dumb-assing around I discovered this.
As for other games, I know the answer is a=b=c for the standard weighted rock, paper, scissors game going by "The Mathematics of Poker", but I cannot get that.
I come up with this when I try to work it:
1) -b+c=a-c => a=-b+2c
2) a-c=-a+b => 2a=b+c =>a=1/2b+1/2c
-3b=-3c => b=c
3b=3c => b=c
the correct answer is a=b=c according to the book. The equation in the up-top example of 2b=2c was not simplified to b=c, so I am pretty sure not simplifying at the end is not the problem.
Where did I mess up?
Sorry, the Physics Forum is just not responding.